Solve x/x+y+x^2/y^2-x^2

$$\frac { x } { x + y } + \frac { x ^ { 2 } } { y ^ { 2 } - x ^ { 2 } }$$

Evaluate

$$\frac{xy}{y^{2}-x^{2}}$$

Short Solution Steps

Factor y^{2}-x^{2}.

$$\frac{x}{x+y}+\frac{x^{2}}{\left(x+y\right)\left(-x+y\right)}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x+y and \left(x+y\right)\left(-x+y\right) is \left(x+y\right)\left(-x+y\right). Multiply \frac{x}{x+y} times \frac{-x+y}{-x+y}.

$$\frac{x\left(-x+y\right)}{\left(x+y\right)\left(-x+y\right)}+\frac{x^{2}}{\left(x+y\right)\left(-x+y\right)}$$

Since \frac{x\left(-x+y\right)}{\left(x+y\right)\left(-x+y\right)} and \frac{x^{2}}{\left(x+y\right)\left(-x+y\right)} have the same denominator, add them by adding their numerators.

$$\frac{x\left(-x+y\right)+x^{2}}{\left(x+y\right)\left(-x+y\right)}$$

Do the multiplications in x\left(-x+y\right)+x^{2}.

$$\frac{-x^{2}+xy+x^{2}}{\left(x+y\right)\left(-x+y\right)}$$

Combine like terms in -x^{2}+xy+x^{2}.

$$\frac{xy}{\left(x+y\right)\left(-x+y\right)}$$

Expand \left(x+y\right)\left(-x+y\right).

$$\frac{xy}{-x^{2}+y^{2}}$$

Factor

$$\frac{xy}{\left(y-x\right)\left(x+y\right)}$$